Elizabeth Proctor fears that Abigail will accuse her just to get her out of the way, and her fears are clearly justified.  She asks John to go to her and make her understand that he will never be with her, that their affair was not an implicit promise of his love, now or in the future.  He doesn't want to go and have this conversation, to acknowledge that such a promise might have been inadvertently made, "Because," he says, "it speaks deceit, and I am honest!"  

Here's the problem: he isn't honest.  At least, not totally.  If he were, he would not have had a secret affair with Abigail Williams in the first place.  His infidelity has proven him to be, at least, capable of dishonesty, and this is a really tough pill for him to swallow.  He desperately wants to be and to be able to think of himself as a good man, a righteous man, and so he says that he is honest.  However, he feels in his heart of hearts that he is no honest man due to his affair, and so he must agree to Elizabeth's request to break his unspoken promise to Abigail because he knows that she is right.  Thus, the internal conflict revealed by this conversation is Proctor's desire to count himself honest in tension with his realization that his own behavior has rendered him just the opposite.